Question

Quadrilateral ABCD is a rectangle. The diagonals intersect at point E. If AE=4x−12 and DB=7x−18 , find x.

Answer 1

ABCD is a rectangle, diagonals are AC and DB.
In a rectangle,
- diagonals bisect each other, AND
- diagonals are equal.

E is the intersection of the diagonals, therefore AE is a half-diagonal,
which means that AE =(1/2)DB, or  
DB=2AE ........................(1)
Substituting values of DB and AE
7x-18=2(4x-12)
solve for x
7x-18 = 8x-24
8x-7x = -18+24
x=6

Answer 2

The point of intersection is the midpoint of the diagonal. The diagonals of a rectangle are the same length. These relationships tell you
2*AE = DB
2*(4x-12) = 7x-18 . . . . . substitute the given information
8x -24 = 7x -18 . . . . . . .eliminate parentheses
x - 24 = -18 . . . . . . . . . .subtract 7x
x = 6 . . . . . . . . . . . . . . . add 24

The value of x is 6.